Introduction¶

From Ddareungi’s perspective, it is important to make the rental bike available and accessible to the public at the right time as it lessens the waiting time. Eventually, providing the city with a stable supply of rental bikes becomes the main objective. Thus, a crucial task is to accurately estimate the bike count required at each hour for the stable supply of rental bikes.

3.1 Data Understanding¶

In [1]:
#Import libraries

import pandas as pd
import numpy as np
from scipy import stats
import statsmodels.api as sm

# use Matplotlib for additional customization
import matplotlib.pyplot as plt
#sets the backend of matplotlib to the 'inline' backend
%matplotlib inline
plt.rcParams['figure.figsize'] = (12,8)

# Seaborn for plotting and styling
import seaborn as sns
sns.set(style="whitegrid")
In [2]:
#import data
bikes = pd.read_csv('SeoulBike.csv', low_memory=False)
bikes.head()
Out[2]:
Date Rented Bike Count Hour Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm) Seasons Holiday Functioning Day
0 1/12/2017 254 0 -5.2 37 2.2 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes
1 1/12/2017 204 1 -5.5 38 0.8 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes
2 1/12/2017 173 2 -6.0 39 1.0 2000 -17.7 0.0 0.0 0.0 Winter No Holiday Yes
3 1/12/2017 107 3 -6.2 40 0.9 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes
4 1/12/2017 78 4 -6.0 36 2.3 2000 -18.6 0.0 0.0 0.0 Winter No Holiday Yes
In [3]:
bikes['Date']
Out[3]:
0        1/12/2017
1        1/12/2017
2        1/12/2017
3        1/12/2017
4        1/12/2017
           ...    
8755    30/11/2018
8756    30/11/2018
8757    30/11/2018
8758    30/11/2018
8759    30/11/2018
Name: Date, Length: 8760, dtype: object

Binning dates

In [4]:
# Convert the 'Date' column to datetime
bikes['Date'] = pd.to_datetime(bikes['Date'], format='%d/%m/%Y')

# Bin the dates into quarters
quarters = pd.cut(bikes['Date'], bins=pd.date_range(start='01/01/2017', end='30/11/2018', freq='Q'))
bikes['quarter'] = quarters

Check rows, columns and data types

In [5]:
bikes.dtypes
Out[5]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Hour                                  int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
Seasons                              object
Holiday                              object
Functioning Day                      object
quarter                            category
dtype: object
In [6]:
bikes.shape
Out[6]:
(8760, 15)
In [7]:
bikes.describe()
Out[7]:
Date Rented Bike Count Hour Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm)
count 8760 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000 8760.000000
mean 2018-05-31 23:59:59.999999744 704.602055 11.500000 12.882922 58.226256 1.724909 1436.825799 4.073813 0.569111 0.148687 0.075068
min 2017-12-01 00:00:00 0.000000 0.000000 -17.800000 0.000000 0.000000 27.000000 -30.600000 0.000000 0.000000 0.000000
25% 2018-03-02 00:00:00 191.000000 5.750000 3.500000 42.000000 0.900000 940.000000 -4.700000 0.000000 0.000000 0.000000
50% 2018-06-01 00:00:00 504.500000 11.500000 13.700000 57.000000 1.500000 1698.000000 5.100000 0.010000 0.000000 0.000000
75% 2018-08-31 00:00:00 1065.250000 17.250000 22.500000 74.000000 2.300000 2000.000000 14.800000 0.930000 0.000000 0.000000
max 2018-11-30 00:00:00 3556.000000 23.000000 39.400000 98.000000 7.400000 2000.000000 27.200000 3.520000 35.000000 8.800000
std NaN 644.997468 6.922582 11.944825 20.362413 1.036300 608.298712 13.060369 0.868746 1.128193 0.436746

3.2 Data Preparation¶

Data preparation (cleaning, transformation, handling duplicates, handling missing values, encoding categorical features, etc.)

In [8]:
bikes.isnull().sum()
Out[8]:
Date                            0
Rented Bike Count               0
Hour                            0
Temperature(°C)                 0
Humidity(%)                     0
Wind speed (m/s)                0
Visibility (10m)                0
Dew point temperature(°C)       0
Solar Radiation (MJ/m2)         0
Rainfall(mm)                    0
Snowfall (cm)                   0
Seasons                         0
Holiday                         0
Functioning Day                 0
quarter                      1464
dtype: int64

Updating Hour Column - 0 to 6 hours: Morning, 7 to 12 hours: Afternoon, 13-18 hrs: Evening, 19-23: Night

In [9]:
# Define a function to categorize hours
def categorize_time(hour):
    if 0 <= hour <= 6:
        return "Morning"
    elif 7 <= hour <= 12:
        return "Afternoon"
    elif 13 <= hour <= 18:
        return "Evening"
    elif 19 <= hour <= 23:
        return "Night"
    else:
        return "Invalid"

bikes['Hour_updated'] = bikes['Hour'].apply(categorize_time)
In [10]:
# Filtered Data Bikes

df = bikes.drop(['Hour'], axis = 1)
In [11]:
df.head()
Out[11]:
Date Rented Bike Count Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm) Seasons Holiday Functioning Day quarter Hour_updated
0 2017-12-01 254 -5.2 37 2.2 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning
1 2017-12-01 204 -5.5 38 0.8 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning
2 2017-12-01 173 -6.0 39 1.0 2000 -17.7 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning
3 2017-12-01 107 -6.2 40 0.9 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning
4 2017-12-01 78 -6.0 36 2.3 2000 -18.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning

Mapping holiday & no holiday to 0 and 1

In [12]:
mapping = {'No Holiday': True, 'Holiday': False}
#Use the replace method to convert to binary
df['Holiday_updated'] = df['Holiday'].replace(mapping)
df.head()
Out[12]:
Date Rented Bike Count Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm) Seasons Holiday Functioning Day quarter Hour_updated Holiday_updated
0 2017-12-01 254 -5.2 37 2.2 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning True
1 2017-12-01 204 -5.5 38 0.8 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning True
2 2017-12-01 173 -6.0 39 1.0 2000 -17.7 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning True
3 2017-12-01 107 -6.2 40 0.9 2000 -17.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning True
4 2017-12-01 78 -6.0 36 2.3 2000 -18.6 0.0 0.0 0.0 Winter No Holiday Yes (2017-09-30, 2017-12-31] Morning True
In [13]:
#Dropping holiday column

df.drop(['Holiday'], axis=1, inplace=True)
In [14]:
df['Seasons'].unique()
Out[14]:
array(['Winter', 'Spring', 'Summer', 'Autumn'], dtype=object)

One hot encoding for Seasons

In [15]:
df2 = pd.get_dummies(df['Seasons'])
In [16]:
df2
Out[16]:
Autumn Spring Summer Winter
0 False False False True
1 False False False True
2 False False False True
3 False False False True
4 False False False True
... ... ... ... ...
8755 True False False False
8756 True False False False
8757 True False False False
8758 True False False False
8759 True False False False

8760 rows × 4 columns

In [17]:
dff = pd.concat([df,df2], axis =1)
In [18]:
dff.drop(['Seasons'], axis=1, inplace=True)
In [19]:
dff
Out[19]:
Date Rented Bike Count Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm) Functioning Day quarter Hour_updated Holiday_updated Autumn Spring Summer Winter
0 2017-12-01 254 -5.2 37 2.2 2000 -17.6 0.0 0.0 0.0 Yes (2017-09-30, 2017-12-31] Morning True False False False True
1 2017-12-01 204 -5.5 38 0.8 2000 -17.6 0.0 0.0 0.0 Yes (2017-09-30, 2017-12-31] Morning True False False False True
2 2017-12-01 173 -6.0 39 1.0 2000 -17.7 0.0 0.0 0.0 Yes (2017-09-30, 2017-12-31] Morning True False False False True
3 2017-12-01 107 -6.2 40 0.9 2000 -17.6 0.0 0.0 0.0 Yes (2017-09-30, 2017-12-31] Morning True False False False True
4 2017-12-01 78 -6.0 36 2.3 2000 -18.6 0.0 0.0 0.0 Yes (2017-09-30, 2017-12-31] Morning True False False False True
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
8755 2018-11-30 1003 4.2 34 2.6 1894 -10.3 0.0 0.0 0.0 Yes NaN Night True True False False False
8756 2018-11-30 764 3.4 37 2.3 2000 -9.9 0.0 0.0 0.0 Yes NaN Night True True False False False
8757 2018-11-30 694 2.6 39 0.3 1968 -9.9 0.0 0.0 0.0 Yes NaN Night True True False False False
8758 2018-11-30 712 2.1 41 1.0 1859 -9.8 0.0 0.0 0.0 Yes NaN Night True True False False False
8759 2018-11-30 584 1.9 43 1.3 1909 -9.3 0.0 0.0 0.0 Yes NaN Night True True False False False

8760 rows × 18 columns

One hot encoding for Hour_updated

In [20]:
df3 = pd.get_dummies(df['Hour_updated'])
In [21]:
df3
Out[21]:
Afternoon Evening Morning Night
0 False False True False
1 False False True False
2 False False True False
3 False False True False
4 False False True False
... ... ... ... ...
8755 False False False True
8756 False False False True
8757 False False False True
8758 False False False True
8759 False False False True

8760 rows × 4 columns

In [22]:
df_updated = pd.concat([dff,df3], axis =1)
In [23]:
df_updated.dtypes
Out[23]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
Functioning Day                      object
quarter                            category
Hour_updated                         object
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
dtype: object
In [24]:
#dropping Hour_updated
df_updated.drop(['Hour_updated'], axis=1, inplace=True)
df_updated
Out[24]:
Date Rented Bike Count Temperature(°C) Humidity(%) Wind speed (m/s) Visibility (10m) Dew point temperature(°C) Solar Radiation (MJ/m2) Rainfall(mm) Snowfall (cm) ... quarter Holiday_updated Autumn Spring Summer Winter Afternoon Evening Morning Night
0 2017-12-01 254 -5.2 37 2.2 2000 -17.6 0.0 0.0 0.0 ... (2017-09-30, 2017-12-31] True False False False True False False True False
1 2017-12-01 204 -5.5 38 0.8 2000 -17.6 0.0 0.0 0.0 ... (2017-09-30, 2017-12-31] True False False False True False False True False
2 2017-12-01 173 -6.0 39 1.0 2000 -17.7 0.0 0.0 0.0 ... (2017-09-30, 2017-12-31] True False False False True False False True False
3 2017-12-01 107 -6.2 40 0.9 2000 -17.6 0.0 0.0 0.0 ... (2017-09-30, 2017-12-31] True False False False True False False True False
4 2017-12-01 78 -6.0 36 2.3 2000 -18.6 0.0 0.0 0.0 ... (2017-09-30, 2017-12-31] True False False False True False False True False
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
8755 2018-11-30 1003 4.2 34 2.6 1894 -10.3 0.0 0.0 0.0 ... NaN True True False False False False False False True
8756 2018-11-30 764 3.4 37 2.3 2000 -9.9 0.0 0.0 0.0 ... NaN True True False False False False False False True
8757 2018-11-30 694 2.6 39 0.3 1968 -9.9 0.0 0.0 0.0 ... NaN True True False False False False False False True
8758 2018-11-30 712 2.1 41 1.0 1859 -9.8 0.0 0.0 0.0 ... NaN True True False False False False False False True
8759 2018-11-30 584 1.9 43 1.3 1909 -9.3 0.0 0.0 0.0 ... NaN True True False False False False False False True

8760 rows × 21 columns

Mapping for Functioning Day

In [25]:
mapping = {'Yes': True, 'No': False}
#Use the replace method to convert to binary
df_updated['func_updated'] = df_updated['Functioning Day'].replace(mapping)
#Dropping Functioning Day
df_updated.drop(['Functioning Day'], axis = 1, inplace = True)
In [26]:
df_updated.dtypes
Out[26]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
quarter                            category
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
func_updated                           bool
dtype: object

3.3 Data Visualization¶

3.3.1 Distribution graphs for numerical columns

In [27]:
# Distribution graph for int/float columns

columns_to_plot = ['Rented Bike Count', 'Temperature(°C)', 'Humidity(%)', 'Wind speed (m/s)', 'Visibility (10m)', 'Dew point temperature(°C)', 'Solar Radiation (MJ/m2)', 'Rainfall(mm)', 'Snowfall (cm)']
for column in columns_to_plot:
    plt.hist(df_updated[column], bins=20, color='blue', edgecolor='black')
    plt.xlabel(column)
    plt.ylabel('Frequency')
    plt.title(f'Histogram of {column} Distribution')
    plt.rcParams['figure.figsize'] = (12,8)
    plt.show()
In [28]:
# Use color cue to indicate evening
sns.scatterplot(data = df_updated, x="Temperature(°C)", y="Rented Bike Count", hue='Evening')
plt.title("Scatterplot to understand evening rides given Rented bike count vs Temperature")
plt.show()

Insight from above plot - For lower temperatures, evening rides are not popular. For higher temperatures, evening rides are popular.

In [29]:
#Plotting Rented bike count against rainfall
sns.scatterplot(data = df_updated, x="Rainfall(mm)", y="Rented Bike Count").set_title("Scatterplot of Rented bike count and Rainfall")
plt.show()
In [30]:
# Use color cue to indicate holiday
sns.scatterplot(data = df_updated, x="Temperature(°C)", y="Rented Bike Count", hue='Holiday_updated')
plt.title("Scatterplot to understand holiday rides given Rented bike count vs Temperature")
plt.show()

Insight from above plot - Irrespective of temperature, on holidays, people take more rides

In [31]:
#Plotting Rented bike count against visibility
sns.scatterplot(data = df_updated, x="Visibility (10m)", y="Rented Bike Count").set_title("Scatterplot of Rented bike count and Visibility")
plt.show()
In [32]:
# Use color cue to indicate holiday
sns.scatterplot(data = df_updated, x="Rainfall(mm)", y="Rented Bike Count", hue='Holiday_updated')
plt.title("Scatterplot to understand Holiday rides given Rented Bike Count vs Rainfall")
plt.show()

Insight from above plot - Within 10 mm rainfall, majority of the rides happen

In [33]:
#Plotting Rented bike count against rainfall
sns.scatterplot(data = df_updated, x="Rainfall(mm)", y="Rented Bike Count").set_title("Scatterplot of Rented bike count and Rainfall")
plt.show()

3.3.2 Bar plot for categorical columns

In [34]:
df_updated.dtypes
Out[34]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
quarter                            category
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
func_updated                           bool
dtype: object
In [35]:
columns_to_plot = ['Holiday_updated', 'Autumn', 'Summer','Spring','Winter','Afternoon','Evening','Morning','Night', 'func_updated']
for column in columns_to_plot:
    counts = df_updated[column].value_counts()
    # plt.bar(counts.index, counts, color='skyblue')
    counts.plot(kind='barh')
    plt.xlabel(column)
    plt.ylabel('Count')
    plt.title('Bar Graph for Categorical Data')
    plt.rcParams['figure.figsize'] = (12,8)
    plt.show()
In [ ]:
In [ ]:

Visualizing to understand if people prefer to bike in morning, afternoon, evening or night.

In [36]:
time_categories = ['Morning', 'Afternoon', 'Evening', 'Night']
counts = [df_updated[time].sum() for time in time_categories]

# Create a pie chart to visualize the distribution
plt.figure(figsize=(8, 6))
plt.barh(time_categories, counts, color='skyblue')
plt.xlabel('Count')
plt.ylabel('Time of Day')
plt.title('Bike Preference by Time of Day')
plt.show()

Insight from above plot - People prefer morning rides.

Visualization to understand if people which season to bike.

In [37]:
season_categories = ['Autumn', 'Summer', 'Spring', 'Winter']
counts = [df_updated[season].sum() for season in season_categories]

# Create a pie chart to visualize the distribution
plt.figure(figsize=(8, 6))
plt.barh(season_categories, counts, color='skyblue')
plt.xlabel('Count')
plt.ylabel('Seasons')
plt.title('Bike Preference by Seasons')
plt.show()

It seems prefer similar across seasons with slightly higher in spring

3.3 - Bivariate Analysis & Hypothesis Testing¶

In [38]:
df_updated.dtypes
Out[38]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
quarter                            category
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
func_updated                           bool
dtype: object
In [39]:
# Scatterplot and add a linear regression model fit 

sns.regplot(x='Temperature(°C)', y='Rented Bike Count', data=df_updated)
plt.title('Correlation between Temperature and Rented Bike Count')
plt.show()

Insight - Strong positive correlation between Temperature and bike rides

In [40]:
# Scatterplot and add a linear regression model fit 

sns.regplot(x='Wind speed (m/s)', y='Rented Bike Count', data=df_updated)
plt.title('Correlation between Wind speed (m/s) and Rented Bike Count')
plt.show()

Insight - Not a strong correlation between wind speed and Rented Bike Count

Heatmap for relationship identification¶

In [41]:
# Create a correlation matrix for the selected columns
correlation_matrix = df_updated[['Rented Bike Count', 'Temperature(°C)', 'Humidity(%)', 'Wind speed (m/s)',
                         'Visibility (10m)', 'Dew point temperature(°C)', 'Solar Radiation (MJ/m2)',
                         'Rainfall(mm)', 'Snowfall (cm)', 'Holiday_updated', 'Autumn', 'Spring',
                         'Summer', 'Winter', 'Afternoon', 'Evening', 'Morning', 'Night', 'func_updated']].corr()

# Set the figure size for the heatmap
plt.figure(figsize=(12, 10))

# Create the heatmap using seaborn
sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', linewidths=0.5)

# Set the title
plt.title('Correlation Heatmap')

# Show the heatmap
plt.show()

Correlation heatmap is quite useful to finalise variables for further analysis.

Winter has a strong negative correlation with rented bike count and temperature has a strong positive correlation.

In [ ]:

**Hypothesis 1: Solar Radiation & Humidity give 2 measures of weather. We want to check if they are different by independent sample t-test**

In [42]:
df_updated.dtypes
Out[42]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
quarter                            category
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
func_updated                           bool
dtype: object
In [43]:
stats.ttest_rel(df_updated['Solar Radiation (MJ/m2)'], df_updated['Humidity(%)'])
Out[43]:
TtestResult(statistic=-259.7177024262324, pvalue=0.0, df=8759)

Insight - p-value low, therefore could not reject null hypothesis. mu solar = mu humidity

**Test if Rented bike count is significantly different for the four seasons.**

Null hypothesis - 𝐻0 :𝜇 =𝜇2=𝜇...=�

In [44]:
from scipy import stats

# Select the data for each season
Autumn = df_updated[df_updated['Autumn']]['Rented Bike Count']
Spring = df_updated[df_updated['Spring']]['Rented Bike Count']
Summer = df_updated[df_updated['Summer']]['Rented Bike Count']
Winter = df_updated[df_updated['Winter']]['Rented Bike Count']

# Perform one-way ANOVA
f_statistic, p_value = stats.f_oneway(Autumn, Spring, Summer, Winter)

# Print the ANOVA results
print('F-statistic: {:.4f}, p-value: {:.4f}'.format(f_statistic, p_value))

F-statistic: 776.4678, p-value: 0.0000

Insight - Could not reject null hypothesis, there is no significant difference between average Rented bike counts for different seasons.*

3.4 - Multiple Linear Regression & Interpreting results¶

In [45]:
df_updated.dtypes
Out[45]:
Date                         datetime64[ns]
Rented Bike Count                     int64
Temperature(°C)                     float64
Humidity(%)                           int64
Wind speed (m/s)                    float64
Visibility (10m)                      int64
Dew point temperature(°C)           float64
Solar Radiation (MJ/m2)             float64
Rainfall(mm)                        float64
Snowfall (cm)                       float64
quarter                            category
Holiday_updated                        bool
Autumn                                 bool
Spring                                 bool
Summer                                 bool
Winter                                 bool
Afternoon                              bool
Evening                                bool
Morning                                bool
Night                                  bool
func_updated                           bool
dtype: object
In [46]:
boolean_columns = ['Holiday_updated','Autumn','Spring', 'Summer', 'Winter', 'Afternoon', 'Evening', 'Morning', 'Night', 'func_updated']
# # Convert the specified Boolean columns to integers
for column in boolean_columns:
    df_updated[column] = df_updated[column]*1
# df['Holiday_update'] = df['Holiday_updated'].astype(int)
# df['Autumn'] = df['Autumn'].astype(int)
# df['Spring'] = df['Spring'].astype(int)
# df['Summer'] = df['Summer'].astype(int)
# df['Winter'] = df['Winter'].astype(int)
# df['Afternoon'] = df['Afternoon'].astype(int)
# df['Evening'] = df['Evening'].astype(int)
# df['Morning'] = df['Morning'].astype(int)
# df['Night'] = df['Night'].astype(int)
# df['func_updated'] = df['func_updated'].astype(int)

Regress Rented Bike Count on Temp, Humidity, Holiday, Rainfall, Evening, Morning, Winter, Solar Radiation, Func_updated

In [47]:
#doing regression on these columns -- summer led to no change in rsquare. 
X_columns = ['Temperature(°C)','Humidity(%)','Holiday_updated','Rainfall(mm)','Evening','Morning','Winter','Solar Radiation (MJ/m2)','func_updated']
X = df_updated[X_columns]
Y = df_updated['Rented Bike Count']
X = sm.add_constant(X)
est = sm.OLS(Y.astype(float), X.astype(float)).fit()
print(est.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:      Rented Bike Count   R-squared:                       0.561
Model:                            OLS   Adj. R-squared:                  0.561
Method:                 Least Squares   F-statistic:                     1245.
Date:                Sun, 12 Nov 2023   Prob (F-statistic):               0.00
Time:                        14:32:14   Log-Likelihood:                -65489.
No. Observations:                8760   AIC:                         1.310e+05
Df Residuals:                    8750   BIC:                         1.311e+05
Df Model:                           9                                         
Covariance Type:            nonrobust                                         
===========================================================================================
                              coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------------
const                     309.3319     37.509      8.247      0.000     235.805     382.859
Temperature(°C)            25.5081      0.622     41.025      0.000      24.289      26.727
Humidity(%)                -9.2000      0.290    -31.701      0.000      -9.769      -8.631
Holiday_updated           100.8054     21.243      4.745      0.000      59.164     142.447
Rainfall(mm)              -66.6663      4.194    -15.898      0.000     -74.887     -58.446
Evening                    86.5068     12.504      6.918      0.000      61.996     111.018
Morning                  -492.2487     11.458    -42.961      0.000    -514.709    -469.788
Winter                   -329.5382     16.319    -20.194      0.000    -361.527    -297.549
Solar Radiation (MJ/m2)  -191.9102      7.278    -26.368      0.000    -206.177    -177.643
func_updated              857.7162     25.502     33.633      0.000     807.726     907.706
==============================================================================
Omnibus:                     1136.530   Durbin-Watson:                   0.464
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2074.836
Skew:                           0.847   Prob(JB):                         0.00
Kurtosis:                       4.678   Cond. No.                         592.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
In [48]:
fig = plt.figure(figsize=(12,8))
fig = sm.graphics.plot_partregress_grid(est, fig=fig)
plt.show()
In [49]:
sns.histplot(est.resid)
plt.xlabel('Residuals')
plt.title('Histogram of Residuals')
plt.show()
In [50]:
# Get the influence analysis results from the fitted model
influence = est.get_influence()
# show the influence analysis summary
# print(influence.summary_table())
In [51]:
(c, p) = influence.cooks_distance
plt.stem(np.arange(len(c)), c, markerfmt=",")
plt.show()
In [52]:
print(est.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:      Rented Bike Count   R-squared:                       0.561
Model:                            OLS   Adj. R-squared:                  0.561
Method:                 Least Squares   F-statistic:                     1245.
Date:                Sun, 12 Nov 2023   Prob (F-statistic):               0.00
Time:                        14:32:17   Log-Likelihood:                -65489.
No. Observations:                8760   AIC:                         1.310e+05
Df Residuals:                    8750   BIC:                         1.311e+05
Df Model:                           9                                         
Covariance Type:            nonrobust                                         
===========================================================================================
                              coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------------
const                     309.3319     37.509      8.247      0.000     235.805     382.859
Temperature(°C)            25.5081      0.622     41.025      0.000      24.289      26.727
Humidity(%)                -9.2000      0.290    -31.701      0.000      -9.769      -8.631
Holiday_updated           100.8054     21.243      4.745      0.000      59.164     142.447
Rainfall(mm)              -66.6663      4.194    -15.898      0.000     -74.887     -58.446
Evening                    86.5068     12.504      6.918      0.000      61.996     111.018
Morning                  -492.2487     11.458    -42.961      0.000    -514.709    -469.788
Winter                   -329.5382     16.319    -20.194      0.000    -361.527    -297.549
Solar Radiation (MJ/m2)  -191.9102      7.278    -26.368      0.000    -206.177    -177.643
func_updated              857.7162     25.502     33.633      0.000     807.726     907.706
==============================================================================
Omnibus:                     1136.530   Durbin-Watson:                   0.464
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2074.836
Skew:                           0.847   Prob(JB):                         0.00
Kurtosis:                       4.678   Cond. No.                         592.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
In [53]:
import sklearn
from sklearn.decomposition import PCA
pca = PCA()
principal_components = pca.fit_transform(X)
principal_components
Out[53]:
array([[ 2.35031119e+01, -1.50237397e+01,  8.13382049e-02, ...,
        -1.21987517e-01,  2.40959105e-02,  0.00000000e+00],
       [ 2.25544302e+01, -1.54579810e+01,  7.11621626e-02, ...,
        -1.20738004e-01,  2.34177393e-02, -0.00000000e+00],
       [ 2.16333644e+01, -1.60901227e+01,  6.16544819e-02, ...,
        -1.18861534e-01,  2.22578186e-02, -0.00000000e+00],
       ...,
       [ 2.04460972e+01, -7.54689974e+00,  7.64783809e-02, ...,
         6.05448896e-03, -8.15310263e-02,  0.00000000e+00],
       [ 1.85349260e+01, -8.31643221e+00,  5.57921155e-02, ...,
         8.24003584e-03, -8.26464942e-02,  0.00000000e+00],
       [ 1.65823312e+01, -8.78911414e+00,  3.41033078e-02, ...,
         9.48514621e-03, -8.30393381e-02,  0.00000000e+00]])
In [54]:
from statsmodels.stats.outliers_influence import variance_inflation_factor
# Calculate VIF
Y = Y.astype(float) 
X = X.astype(float)
vif = pd.DataFrame()
vif["VIF Factor"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]
vif["features"] = X.columns

# Inspect VIF Values, round it to 2 decimal places
vif.round(2)
Out[54]:
VIF Factor features
0 67.49 const
1 2.65 Temperature(°C)
2 1.67 Humidity(%)
3 1.01 Holiday_updated
4 1.07 Rainfall(mm)
5 1.41 Evening
6 1.30 Morning
7 2.37 Winter
8 1.92 Solar Radiation (MJ/m2)
9 1.02 func_updated
  1. Overall fit of the model: 56.1% of variance is explained by regression model
  2. Regression equation: Rented bike count = 25.5Temperature(°C) + (-9.2)Humidity(%) + (100.8054)Holiday_updated + (-66.66)Rainfall(mm) + (86.51)Evening + (-492.25)Morning + (-329.5382)Winter + (-191.91)Solar Radiation (MJ/m2) + (857.72)*func_updated + 309.3319
  3. Significance of individual variables and regression coefficients: All variables have P value less than 0.05 so they are statistically significant.
  4. Check if there is any violations of model assumptions: Residuals are normally distributed around zero. The residual vs. predicted value plot shows no autocorrelation. The variance of residuals is also approximately constant.
  5. Check if there is any influential observations: All cook's d scores are less than 1. No outlier
  6. Check if there is any multicollinearity issue: VIF values are within - 1 < VIF < 10: moderate correlation, but it is not severe to warrant corrective measures.
In [ ]:

Vision with respect to how analytics can help provide additional insights¶

As you describe your analytics vision for Ddareungi, please be specific with respect to:

A. Holiday Impact 1) How do holidays affect bike rentals, and should we adjust bike availability on holidays? 2) Historical rental data and holiday information. 3) Visual analytics of rental patterns on holidays vs. regular days and machine learning to predict holiday-specific demand.

B. Promotion and Marketing 1) Can we identify opportunities for promoting bike rentals during specific hours or under certain weather conditions to increase revenue? 2) Marketing campaigns data, and user feedback. 3) Regression analysis to find associations between rentals and marketing efforts, and A/B testing to measure the impact of promotions.

C. Competitive Benchmarking 1) How does Ddareungi's bike rental service compare with competitors, and how can we gain a competitive advantage? 2) Data on competitors' services and user feedback. 3) Comparative analysis of service quality, pricing, and user satisfaction to identify areas for improvement.data

In [ ]: